I had a look at the Gustaf Wilhelm Söderberg that I found on the online Swedish church books and found the below. It looks like he used his mothers maiden name at the time of emigration. He also had two sisters that emigrated which may help you determine if its the right man or not
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Stora Mellösa AI:20b (1851-1855) Bild 316 / sid 310 (AID: v52364.b316.s310, NAD: SE/ULA/11458)
1851-1855, Börsholm, Ekeby Rote, Stora Mellösa, Örebro län, Närke
Lars Larsson, b. 22 JUL 1825 in Stora Mellösa, Örebro län, Närke.
Amanda Amalia Söderberg, b. 11 MAR 1822 in Glanshammar, Örebro län, Närke
Their children
Johan Erik, b. 25 APR 1842 in Glanshammar, Örebro län, Närke
Gustaf Wilhelm, b. 24 JUL 1848 in Stora Mellösa, Örebro län, Närke
Christina Amalia, b. 4 MAY 1850 in Stora Mellösa, Örebro län, Närke.
Carolina Justina, b. 15 JUN 1854 in Stora Mellösa, Örebro län, Närke.
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Stora Mellösa AI:21b (1856-1860) Bild 273 / sid 266 (AID: v52366.b273.s266, NAD: SE/ULA/11458)
1856-1860, Börsholm, Ekeby Rote, Stora Mellösa, Örebro län, Närke
Lars Larsson, b. 22 JUL 1825 in Stora Mellösa, Örebro län, Närke. Dies 30 JUN 1856.
Amanda Amalia Söderberg, b. 11 MAR 1822 in Glanshammar, Örebro län, Närke
Their children
Johan Erik, b. 25 APR 1842 in Glanshammar, Örebro län, Närke
Gustaf Wilhelm, b. 24 JUL 1848 in Stora Mellösa, Örebro län, Närke
Christina Amalia, b. 4 MAY 1850 in Stora Mellösa, Örebro län, Närke.
Carolina Justina, b. 15 JUN 1854 in Stora Mellösa, Örebro län, Närke. Dies 28 MAY 1857.
Amanda has another child after her husbands death
Johanna Augusta, b. 7 JAN 1860 in Stora Mellösa, Örebro län, Närke
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Stora Mellösa AI:22b (1861-1865) Bild 286 / sid 278 (AID: v52368.b286.s278, NAD: SE/ULA/11458)
1861-1865, Börsholm, Ekeby Rote, Stora Mellösa, Örebro län, Närke
The widow, Amanda Amalia Söderberg, b. 11 MAR 1822 in Glanshammar, Örebro län, Närke
Her children from the marriage
Gustaf Wilhelm, b. 24 JUL 1848 in Stora Mellösa, Örebro län, Närke (it says that he was born in Glanshammar here, but that is wrong)
Christina Amailia, b. 4 MAY 1850 in Stora Mellösa, Örebro län, Närke.
Amandas children after her husband passed away
Johanna Augusta, b. 7 JAN 1860 in Stora Mellösa, Örebro län, Närke
Triplets
a female child, b. 8 DEC 1864 in Stora Mellösa, Örebro län, Närke. Died 10 DEC 1864
Maria, b. 8 DEC 1864 in Stora Mellösa, Örebro län, Närke. Died 30 DEC 1864
Axel, b. 8 DEC 1864 in Stora Mellösa, Örebro län, Närke. Died 4 JAN 1865
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Stora Mellösa AI:27aa (1886-1890) Bild 74 / sid 65 (AID: v52404.b74.s65, NAD: SE/ULA/11458)
Amanda Amalia Söderberg, b. 11 MAR 1822 in Glanshammar, Örebro län, Närke. Remarries 2 AUG 1868 to
Anders Olsson Bergman, b. 30 APR 1812 in Stora Mellösa, Örebro län, Närke
Amanda dies 10 JAN 1890 at Östra Rynninge, Stora Mellösa, Örebro län, Närke
Anders dies 5 OCT 1886 at Östra Rynninge, Stora Mellösa, Örebro län, Närke
Askers häradsrätt AIIa:55 (1890-1890) Bild 306 / sid 303 (AID: v144824.b306.s303, NAD: SE/ULA/10026)
The estate inventory after Amanda says that Gustaf and the daughter Johanna Augusta (married to B. Magnusson) are living in Aurora in North America. It says that the daughter Amalia is living is Stockholm (which is where she emigrated from, see below) and that her son, Johan Erik Hellstrand (he must have picked another last name) has passed away and left behind two daughters Hedvig and Ellin in Örebro.
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I found the following on the Swedish emigration DVD, EMIBAS
Gustaf Vilhelms sister
Christina Amalia Larsson, b. 4 MAY 1850 in Stora Mellösa, Örebro län, Närke. Emigrated 2 JUL 1891 from Kolmätargränd 2, Västerlånggatan 10, Storkyrkoförsamlingen, Stockholms stad, Uppland to north America. Single at the time of emigration.
Gustaf Vilhelms half sister
Johanna Augusta Söderberg, b. 7 JAN 1860 in Stora Mellösa, Örebro län, Närke
Emigrated 29 JUN 1888 from Hensbyn, Fröskog, Älvsborgs län, Dalsland with her children (her husband left ahead of them)
The children
Alfred Victorinus, b. 25 FEB 1880 in Högbo, Gävleborgs län, Gästrikland
Ture Julius, b. 1 OCT 1882 in Högbo, Gävleborgs län, Gästrikland
Knut Anton, b. 30 MAY 1885 in Högbo, Gävleborgs län, Gästrikland
Johanna Augusta Söderbergs husband
Bengt Enoch Magnusson, b. 17 SEP 1855 in Fröskog, Älvsborgs län, Dalsland. Emigrated 21 FEB 1887 from Sandviken, Högbo, Gävleborgs län, Gästrikland to Aurora, USA.
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Anna
I am not related to this family